This repository was archived by the owner on Jul 24, 2024. It is now read-only.
feat(library): weak duality of max-flow min-cut theorem#18996
Open
feat(library): weak duality of max-flow min-cut theorem#18996
Conversation
LaTeX is used.
Implemented in LaTeX
eric-wieser
reviewed
May 12, 2023
leanpkg.toml
Outdated
| path = "src" | ||
|
|
||
| [dependencies] | ||
| mathlib = {git = "https://github.com/leanprover-community/mathlib", rev = "290a7ba01fbcab1b64757bdaa270d28f4dcede35"} |
Member
There was a problem hiding this comment.
This doesn't make any sense in mathlib itself!
eric-wieser
reviewed
May 12, 2023
Comment on lines
+814
to
+821
| -- /-! | ||
| -- Here is our second big lemma, if the active flow is maximum, | ||
| -- then no augmenting path exists in the residual network. | ||
| -- -/ | ||
|
|
||
| -- lemma no_augm_path {V : Type*} [inst' : fintype V] | ||
| -- (rsn : residual_network V) : (is_max_flow rsn.afn) -> no_augmenting_path rsn := | ||
| -- begin |
Member
There was a problem hiding this comment.
If this is intended to be part of a later PR, you should just delete it from this one.
eric-wieser
reviewed
May 12, 2023
Member
There was a problem hiding this comment.
This should either be:
- Hosted on your own website / arxiv, and linked from
references.bib - Put in the module docstring, or in various smaller docstrings throughout the file. Note that the doc website supports LaTeX in
$$s
eric-wieser
reviewed
May 12, 2023
| (is_edge : V → V → Prop) | ||
| (nonsymmetric : ∀ u v : V, ¬ ((is_edge u v) ∧ (is_edge v u))) | ||
|
|
||
| structure capacity (V : Type*) [inst : fintype V] |
Member
There was a problem hiding this comment.
To me this looks like it would work better as
Suggested change
| structure capacity (V : Type*) [inst : fintype V] | |
| structure capacity {V : Type*} [inst : fintype V] (g : digraph V) |
Which says "a capacity on a particular graph". I assume you don't ever need to compare capacities between different graphs?
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to subscribe to this conversation on GitHub.
Already have an account?
Sign in.
3 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Formalise and validate the weak duality of the max-flow min-cut theorem, i.e. the value of every flow is less than or equal to the capacity of every cut.
The rest of the max-flow min-cut theorem proof is commented out because it contains sorry.